CONSTRUCTION OF THE SYSTEMS WITH A PERTURBED LINEAR CENTER HAVING NO MORE THAN ONE LIMIT CYCLE
Abstract
The problem under our consideration is to construct systems with a perturbed linear center of special form that have no more than one limit cycle in the entire phase plane for all real values of the perturbation parameter μ. To solve this problem, we have proposed a method for constructing a Dulac – Cherkas function as a second-degree polynomial with respect to a phase variable y, whose coefficients smoothly depend on the second-phase variable x and continuously depend on the parameter μ. The construction of the Dulac – Cherkas function is based on reducing the auxiliary polynomial Φ(x,y,μ) to the function Φ0(x,μ) depending only on the variable x and the parameter μ. A regular method for such reduction is proposed. Examples of the constructed systems having a unique limit cycle in the entire phase plane are presented.
About the Authors
A. V. Kuzmich
Yanka Kupala State University of Grodno
Belarus
Belarus
Senior Lecturer of the Department of Fundamental and Applied Mathematics, Faculty of Mathematics and Informatics
A. A. Hryn
Yanka Kupala State University of Grodno
Belarus
Belarus
D. Sc. (Physics and Mathematics), Assistant Professor, Head of the Department of Mathematical Analysis, Differential Equations and Algebra, Faculty of Mathematics and Informatics
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